BRUSSELS (Reuters) - If Washington's European allies had any hope that Donald Trump would sound less like Donald Trump now that he is days from the U.S. presidency, his first European newspaper interview quickly buried it.

Trump declared the NATO alliance "obsolete", praised Britain's exit from the European Union and gave his clearest hint yet that he would consider lifting financial sanctions on Moscow, which the United States and EU both imposed after Russia seized Ukraine's Crimea peninsula.

His new remarks drew public expressions of dismay from across Europe. German Foreign Minister Frank-Walter Steinmeier said they had led to "astonishment and agitation" in Brussels, where Steinmeier was meeting EU counterparts. He said he had already met with the head of NATO to share his concern.

The EU executive, however, voiced confidence that Trump would come round to seeing it as the key U.S. ally it had been for decades: "I'm sure that sooner or later everyone in Washington will understand that it's in the strategic interests of the United States to have a successful European Union," European Commission deputy head Frans Timmermans told CNN.

And behind the scenes, European officials say they are still confident that the architecture of the Western security alliance will survive a Trump presidency.

Many say they have taken heart from the more conventional foreign policy positions described by Trump's picks for defense secretary and secretary of state, General James Mattis and Exxon-Mobil ex-CEO Rex Tillerson, at confirmation hearings. They also point to the strong support for NATO and the firm line on Russia expressed by senators from Trump's Republican Party during the questioning.

Ultimately, they expect the post-World War Two Western alliance to withstand a more sceptical approach from the White House, thanks to deep institutional understanding of its benefits on both sides of the Atlantic. A stepped-up schedule of summits and meetings will give early chances to clear the air.

"We are working on the basis that Trump will listen to Mattis, Tillerson and foreign policy Republicans," said a senior EU diplomat involved in foreign policy planning in Brussels.

"If we can cement a relationship based around the calendar of meetings, bilaterals and summits, we may be able to get beyond the headlines and the election campaign."

FOCUS ON EUROPE

Trump takes charge of U.S. foreign policy and becomes commander-in-chief of the military at a time when the 2014 Ukraine crisis has already prompted Washington and NATO to shift their focus from the wars in Afghanistan and Iraq back towards the founding mission of defending Europe.

Three years after the last U.S. tank left Europe, U.S. heavy weaponry is returning as part of a congressionally-approved $3.4 billion spending plan to increase Europe's defenses against what NATO -- led by U.S. strategists -- sees as an increasingly aggressive Russia.

Under that plan, the U.S. army will deploy thousands of troops in Poland and the Baltic states of Latvia, Lithuania and Estonia, which all fear that Russia could attempt a land-grab on the model of its operation in Ukraine.

The head of the Latvian parliament's foreign affairs committee, Ojars Eriks Kalnins, told Reuters his country was reassured by Mattis's confirmation hearings last week.

"If you listen to his testimony then everything fits with our positions," he said.

The first big chance to solidify the alliance will come Feb. 15-16, when Mattis is expected to make his debut at NATO headquarters in Brussels for a meeting of alliance ministers.

That will be quickly followed by the annual Munich Security Conference in the German city, normally attended by world leaders and cabinet ministers, at which EU officials can press Trump administration figures for their views.

A second senior EU official working on EU foreign policy said there will also be a swift invitation for Tillerson to attend an EU foreign ministers meeting in Brussels.

"We obviously plan to engage with the incoming US administration, it'll be important to assess our common priorities."

Trump himself could make his European summit debut at a NATO meeting in April or May, although it has not yet been scheduled and could wait until 2018. Otherwise, he will share a stage with the British, Canadian, French, German, Italian and Japanese leaders at a G7 summit in Italy in May.

Czech Foreign Minister Lubomir Zaoralek said the main strategy was to ensure lines of dialog are open between the new administration and allies on the continent.

"I'm convinced it's about communication," he said. "Our role is to be active, it's not a wait-and-see strategy. For all of us, it's very important to address partners in this new structure and to start cooperation and exchange of views."

European officials say they expect Trump to hear about the importance of the U.S.-European alliance not only from diplomats and generals, but from fellow businessmen who recognize the need for close ties with the world's biggest trading bloc.

Trump "would be well-advised to ask his international American companies how much sense it makes to operate in a single market in Europe. Then perhaps a sense of understanding would prevail," said Johannes Hahn, the European Commissioner in charge of the bloc's future expansion.

Still, despite the reassurance Europeans take from Trump's cabinet picks, one EU diplomat said the conclusion in Brussels was that they were dealing with "a big unknown" in Trump himself. "Whatever Tillerson, Mattis and others say, it is not necessarily the new administration's policy."

French Foreign Minister Jean-Marc Ayrault said Europe could learn a valuable lesson from a sceptical Washington: European countries need to stick together to defend themselves.

"The best way to defend Europe, that's what Mr. Trump is inviting us to do, is to remain united, is to stand together and not forget that the strength of Europeans is their unity," Ayrault said.

(Additional by Robert-Jan Bartunek, Philip Blenkinsop, Alastair Macdonald and Tom Korkemeier in Brussels, David Mardiste in Tallinn and Gederts Gelzis in Riga; Editing by Peter Graff)